13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- ( ) ( ) , , 2 2 σ ε ε ε ε ′ ′ = + = +b c f a a el a pl f N N E (11) εa is the strain amplitude. , εa el and , εa pl are the elastic and plastic part for the strain amplitude. E is the Young’s modulus. N is the fatigue life, it stands for fatigue crack initiation life or fatigue fracture life. Here it means the fatigue crack initiation life. σ′f is the fatigue strength coefficient. b is the fatigue strength exponent. ε′f is the fatigue ductility coefficient. c is the fatigue ductility exponent. Values are taken from reference [21] and shown in Table 2. Table 2. Experimental strain-life curve parameters Material E(MPa) σf'(MPa) εf' b c S460N 208000 1218 0.452 -0.104 -0.536 In the previous section, the influence rules of the damage controlling parameters A and m are discussed. By fitting the simulation results to the experimental strain-life curve, the parameters A and m can be determined. Here the simulation model is also two plane strain elements connected by one cohesive element. The loading condition and the material behaviour are like in the previous section. The investigations just focus on the very low cycle fatigue regime, so the calculated number of cycles is within 600. For material S460N, the parameters A and m are fitted as: A=25, m=3.7. The experiment and simulation results are plotted in Figure 4. 1 10 100 1 10 100 1000 total strain range(%) number of cycles S460N regression from eq.(11) experimental data CZM simulation Figure 4. Comparison of strain-life curve for material S460N 4.3. Fatigue crack propagation simulation For the material S460N, the damage parameters are determined: λ=1.2, A=25 and m=3.7. These parameters need further validation. As an important part of fatigue fracture, the fatigue crack growth simulation is applied here to validate the damage parameters. The experimental data of fatigue crack growth for the material S460N are taken from reference [22]. The experimental fatigue crack growth rate curve includes four different strain range levels, i.e. Δε=0.4%, Δε=0.6%, Δε=1.0% and Δε=2.0%. Because the investigations focus on very low cycle fatigue regime, just the experimental data at fast crack growth rate are used for comparison. The numerical model is a two dimensional compact tension specimen. The dimension of the model is width 50mm and height 60mm. The initial crack length a0 is 25mm and the ligament length is 25mm, too. The type of the continuum element is plane strain. The material behaviour of the continuum elements is the same as in the previous section. The cohesive elements locate along the
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